All the cities on the Barbados map are yellow, so they recieve yellow cubes, right? Can any of these cities be converted to "New Cities" as well or is that action reserved only for the "Town" spaces? I am new to the game and the solo map looks a bit different than the main one. Am I the only one confused?

If by "receive" you mean you have to deliver yellow cubes to them to generate income then yes. Set up is random as normal. Only the towns can be converted to new cities. Since there are only 10 turns and you have to use each of the 4 available actions before they become available again this means the maximum number of new cities in a game will be 3.